login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A306645 a(n) is the least positive multiple of n belonging to A306263 if any, or a(n) = -1 otherwise. 1
1, 2, 6, 4, 10, 6, 42, 8, 18, 10, 66, 12, 156, 42, 60, 16, 34, 18, 228, 20, 42, 66, 92, 24, 300, 156, 108, 84, 116, 60, 310, 32, 66, 34, 420, 36, 222, 228, 156, 40, 246, 42, 172, 132, 180, 92, 2820, 48, 588, 300, 204, 156, 212, 108, 660, 168, 228, 116, 590, 60 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Is a(n) > 0 for every n > 0?

LINKS

Table of n, a(n) for n=1..60.

FORMULA

a(A306263(n)) = A306263(n) for any n > 0.

EXAMPLE

For n = 7:

- the divisors of 7 are: 1, 7,

- the corresponding Hamming weights are: 1, 3,

- 3 does not divide 7,

- the divisors of 3*7 are: 1, 3, 7, 21,

- the corresponding Hamming weights are: 1, 2, 3, 3,

- 2 does not divide 3*7,

- the divisors of 2*3*7 are: 1, 2, 3, 6, 7, 14, 21, 42,

- the corresponding Hamming weights are: 1, 1, 2, 2, 3, 3, 3, 3,

- they all divide 2*3*7,

- hence a(7) = 2*3*7 = 42.

MATHEMATICA

With[{s = Select[Range[3000], With[{k = #}, AllTrue[Divisors@ k, Mod[k, DigitCount[#, 2, 1]] == 0 &]] &]}, Table[SelectFirst[s, Mod[#, n] == 0 &] /. k_ /; MissingQ@ k -> -1, {n, 60}]] (* Michael De Vlieger, Mar 05 2019 *)

PROG

(PARI) a(n) = while (1, my (m=n); fordiv (m, d, m = lcm(m, hammingweight(d)); ); if (n==m, return (n), n = m))

CROSSREFS

Cf. A000120, A306263.

Sequence in context: A238642 A145019 A066678 * A113571 A119018 A264647

Adjacent sequences:  A306642 A306643 A306644 * A306646 A306647 A306648

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Mar 03 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 13 06:02 EDT 2021. Contains 342935 sequences. (Running on oeis4.)